We propose a multichannel speech enhancement method using a long short-term memory (LSTM) recurrent neural network. The proposed method is developed in the short time Fourier transform (STFT) domain. An LSTM network common to all frequency bands is trained, which processes each frequency band individually by mapping the multichannel noisy STFT coefficient sequence to its corresponding STFT magnitude ratio mask sequence of one reference channel. This subband LSTM network exploits the differences between temporal/spatial characteristics of speech and noise, namely speech source is non-stationary and coherent, while noise is stationary and less spatially-correlated. Experiments with different types of noise show that the proposed method outperforms the baseline deep-learning-based full-band method and unsupervised method. In addition, since it does not learn the wideband spectral structure of either speech or noise, the proposed subband LSTM network generalizes very well to unseen speakers and noise types.